The incidence of male infertility has kept increasing year by year, severely affecting the sustainability of society. Sperm morphological analysis plays an important role in assessing sperm fertility. However, current sperm morphological analysis is usually performed using microscopic images of stained sperm, which requires complex staining operations, making it difficult to achieve a comprehensive and efficient diagnosis. In this work, we propose and experimentally demonstrate sperm morphological analysis with optofluidic time-stretch (OTS) imaging flow cytometry. Specifically, we capture the stain-free sperm images with high-throughput OTS imaging flow cytometry and analyze the morphological features using a U-Net network. The analysis of 40,000 images from 20 clinical semen samples indicates that our method achieves higher accuracy than the smear test and shows high concordance with the results using comprehensive methods of routine semen examination. This work provides a high-throughput, stain-free sperm morphological analysis method, which holds promise for a comprehensive evaluation of semen.